Question

In a PSK system, the bit rate is 1 Mbps and $N_0=0.5\times {10}^{-12}W/Hz$. The amplitude of the waveform if probability of error, $P_e={10}^{-3}$ will be______ (in mV).

$\left[givenerfc\right(2.8)=2\times {10}^{-3}]$

• A. 2.8

Answer 1

The correct option is A 2.8
For PSK system $P_c=\frac{1}{2}erfc\left[\sqrt{\frac{A_c^2{T}_b}{2N_0}}\right]$

$\Rightarrow {10}^{-3}=\frac{1}{2}erfc\left[\sqrt{\frac{A_c^2{T}_b}{2N_0}}\right]$

$\Rightarrow 0.002=erfc\left[\sqrt{\frac{A_c^2{T}_b}{2N_0}}\right]\Rightarrow \frac{A_c^2{T}_b}{2N_0}=(2.8{)}^2$

$\Rightarrow \frac{A_c^2}{2\times 0.5\times {10}^{-12}\times {10}^6}=(2.8{)}^2$

$\Rightarrow A_c=2.8mV$